My concept of a reusable (sc)ramjet shuttle would be something like this.

The fuselage is a cylinder, perhaps 70 meters in length and 10 meters in diameter. The entire front of the fuselage is the air scoop; the entire rear is the exhaust expansion cone. The two funnels would have a length of perhaps 10 meters (and a diameter of 10 meters as well). Nearly all of the shockwave will be inhaled by the air scoop, in which it will bounce around and be directed successively rearwards by repeated reflections. Thus, the shockwave will be used to compress the inhaled air. The interior looks like two funnels placed small end to small end, with a long neck. The fuel, machinery, crew space (if any), and payload are in the space between the two funnels (air scoop and expansion cone) and the cylindrical exterior. There will also be wings and control surfaces attached to the fuselage.

Fuel (hydrogen) is injected at the front of the cylindrical neck, which is 50 meters long. It mixes and burns in this neck, with complete ignition insured by means of microwaves causing intermittent glow discharge in the compressed air-fuel mixture.

The portions of the cones and the exterior that receive the greatest amount of heat per unit area would be cooled by liquid hydrogen on its way to the engine. This has worked very well in liquid fueled rockets.

I conceive that the portion of the surface that would be exposed to the highest temperatures would be made of superalloy, similar or more refractory than aircraft exhaust turbines. Some alloy largely composed of Ta, W, Re, Os, and Ir would probably be suitable, melting at well over 2200 C. Other portions would be made of suitable alloys for their particular temperature regimes. Probably some lighter alloy from Nb, Mo, Ru, and Rh would work for intermediate temperature areas.

There is plenty of time during the transit through the 50 meter neck for fuel to burn before expansion begins.

The engine would be designed to operate in subsonic and supersonic combustion modes, with smooth transition between them.

At least, that is how I see things at this point.